I'm getting great results printing multiple objects in Ninjaflex on the TAZ6 with Aerostruder. Actually, I'll getting prints that look as good or better than PLA prints!
I'm attaching the profile I'm using for some small parts that have no infill and 1mm walls, but the infill can be added and wall thickness and layer heights can be changed with good results.

The key factors are the bed temperature and the fan speed. I start the print with a bed temp of 60C and reduce to 50C after the first layer. 40C (as in the Ninjaflex stock profiles) is too low! Use 50C at least.

The fan speed settings start at 0% and the fan is set to start at the 5mm height. The reason for this is that the Aerostruder fan is over-cooling the thermistor when it is close to the print bed. Apparently the airflow is bouncing off the bed to the thermistor. As the print progresses away from the bed the chances of thermal runaway are greatly reduced. You can see the difference in the reported temperature when the fan starts -- you'll see it start to drop, then begin to rise again as higher layers are printed. So if that cooling is too great, the thermistor reports a much cooler temperature and more power is applied to the hot end heater and this causes a thermal runaway condition and the print stops. Remember, the temperature reported on the LCD is the temperature of the thermistor, not the hot end! Higher bed temperatures and lower (or even zero) fan speeds help prevent the thermal runaway condition. Using the attached profile I get absolutely no stringing between multiple parts.

I've downloaded and imported the profile but I cannot get it to show up in Cura. I'm using 3.2.27 and it won't show up in the profile list. I've tweaked the ninjaflex profile myself and I wanted to see how yours compared.